Monopoles and solitons in fuzzy physics

Monopoles and solitons have important topological aspects like quantized fl uxes, winding numbers and curved target spaces. Naive discretizations which substitute a lattice of points for the underlying manifolds are incapable of retaining these features in a precise way. We study these problems of di screte physics and matrix models and discuss mathematically coherent discre tizations of monopolies and solitons using fuzzy physics and noncommutative geometry. A fuzzy sigma-model action for the two-sphere fulfilling a fuzzy Belavin-Polyakov bound is also put forth.